How do you define variables directly in a play, and how do you load them from a separate file instead?

Put them in a vars: block at the start of the play, or list external YAML files under vars_files: (paths relative to the playbook). Either way they become play variables, usable in every task of that play.

- hosts: all
  vars:
    user: joe
    home: /home/joe
  tasks: ...

- hosts: all
  vars_files:
    - vars/users.yml

and vars/users.yml contains plain key-value pairs, with no play structure around them:

user: joe
home: /home/joe

Why move variables out into a file? The playbook stays short and readable, the same variable file can be shared between playbooks, and, most importantly, a file can be encrypted with Ansible Vault while the playbook stays readable. That is the usual way to keep passwords out of plain-text playbooks.

Go deeper:

• Defining variables in included files and roles (official docs) — vars, vars_files and where each fits.